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At 1414 GMT, Orange shares were up 2.2 percent, at the top of France's CAC 40, while Deutsche Telekom rose 2.5 percent to the top of the DAX.
The report said there were "confidential discussions" held between the two companies examining the options for a "merger of equals".
Telecoms stocks across the region traded higher, with the industry's index up 1.6 percent, leading sector gains.
Deutsche Telekom and Orange declined to comment on the report.